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• Levels of students' understanding on infinity

  317-337

  Markku S. Hannula

  Erkki Pehkonen

  Hanna Maijala

  Riitta Soro

  Views:

  4

  Here we report some results of a two-year study for grades 5-6 and 7-8 (during the academic years 2001-03). The study included a quantitative survey for approximately 150 Finnish mathematics classes out of which 10 classes were selected to a longitudinal part of the study. Additionally, 40 students from these classes participated also a qualitative study. This paper will focus on students' understanding of infinity and the development of that understanding. The results show that most of the students did not have a proper view of infinity but that the share of able students grew, as the students got older.

• Cognitive conflict as a tool of overcoming obstacles in understanding infinity

  279-295

  Jiří Cihlář

  Petr Eisenmann

  Magdalena Krátká

  Petr Vopĕnka

  Views:

  6

  This paper, based on current research, is devoted to obstacles that appear in the process of understanding the concept of infinity. In its introductory part the fundamental types of epistemology obstacles are formulated. The cognitive conflict and its role in overcoming these obstacles are analysed in the following section of this research. Finally, the authors focus on research methodology and the results of the three-year research project. The problems are illustrated by means of real experimental interviews.

• Summe einer unendlichen geometrischen Reihe im Mathematikunterricht

  229-240

  Ján Gunčaga

  Views:

  7

  This article deals with sums of infinite geometric series. We focus on the understanding of the notion by pupils at secondary school through generic and universal models. In the first part we survey this notion in the Czech and Slovak curriculum. We describe the process of gaining knowledge as a sequence of five stages. In the second part we show one possible approach how to introduce the notion "sum of the infinite geometric series" through this process. We illustrate this on some examples for pupils. At the end we formulate some pedagogical recommendation for teachers.